Although the optimal value of \(\tilde{\mathcal {L}}^{(s)}\)  given tree structure \(q_s(\mathbf {x})\)  can be calculated,
to make a trade-off between computational complexity and model performance, a greedy strategy that constructs a tree starting from a single leaf (root) and splitting the leaf into two child leaves iteratively is commonly used [1]}, [2]}, [3]}.
The samples at a leaf will be separated by the split condition defined as a threshold value of one feature, which is the so-called feature-wise split.
Such a greedy search algorithm is included in most GBDT implementations [4]}, [5]}, [3]}, it selects the best split node by node, and finally construct a decision tree.
